This explanation is not correct. It is indeed more likely that 'ing' comes after 'learn' than to have 'learn' come before 'ing'; however, if you take into account the probability of seeing 'ing' at the end of a word, it is higher than that of seeing 'learn' at the beginning of the word; if you compute the probabilities one way or another, you will get exactly the same. So it's not about the probabilities in a language being higher one way or another (they are *exactly the same*, when multiplying the conditional probabilities), it's about them being harder to learn (or to compute). Also, this appears to not be so much related to the syntactic structure of the language, as the effect is universal across languages and is mostly apparent when the context window size gets large (at which scale the orders of the words in a sentence become less relevant, since it is at the scale of quite a few sentences)

​@@mesdamessoleils9869 I'm not quite sure how you computed the probabilities or why you even used that example to get the point across as it might not even be relevant to how a transformer works. Just curious though, how much experience do you have with knowing how transformers work inside out? I myself just learned recently and not 100% clear, nor am not sure of the model or the exact way they did it exactly, but if I have access to the source code, would probably be able to figure this out (rather just theories). However, judging by what I know, the model is trains and predicts a token based on the previous tokens passed into it. So even if I know that at the end of the word, "ing" happens more at the end of the word, I still would have more trouble predicting the root word ("learn" ) behind it rather than predicting "ing" comes after "learn". Just imagine it in terms of possible branches. Obviously, the more choices of likely words to choose from, the less probability for you to predict the next word correctly. Lets say make an example sentence, "I like learning math from my teacher" and the standard tokens are probably "I", "like", "learn", "ing", "math", "from", "my", "teacher". Moreover, assume that the model is trained with a bit more grammatically correct examples. Once my model generates up to the point, "I like learn", the next possible token that makes grammatically correct is easily going to be "ing" or something of high affinity if I use a different example. However, training it backwards, if I predicted "math from my teacher," I'm split between whether I should use a suffix ("ing") or ("learn") because each of them sounds grammatically plausible. Predicting backwards on a larger trained model, I can reasonably get the sentence "I like to learn math from my teacher" or "I like learning math from my teacher". As you can see, there are two plausible options predicting backwards which basically splits the probability of a confident prediction in two while going forwards, it most definitely is easier to complete the puzzle simply following the context clues (which GPTs are basically made for). I might not have exhausted all the cases, but you can probably see what I mean now. From that stand point, it's generally easier to predict forwards than backwards as you can see with english, and you can see this even more when you look at the syntactic structure of English. Generally speaking, we can predict that a good deal of english sentences start with a noun (aka subject or pronouns such as "I") while english sentences can end in a plethora of ways (nouns, verbs, words with suffixes which acts as a token of its own), making the amount of plausible choices that much more when trying to predict backwards. This mass of choices lowers the probability (aka certainty) that we have a confident right answer, hence unequal probabilities forward and back. Moreover, I think the video pretty much is mentioning what I am mentioning through various abstract examples, such as timestamp 6:36 for example. He pretty much says that it's much harder to predict the factors of a product rather than predict the product from the two factors, which completely makes sense. In essence, the models are struggling to learn backwards probably IS in fact since it's harder to learn/solve backwards, and the metric that shows that is the unequal joint probabilities of the sentence forward and back. I looked into the paper and video and found that the loss difference IS infact calculated by the joint probabilities instead, yet they are not the same. Moreover, the conditional probabilities are definitely most likely different forward and back given they are completely different conditional probabilities (NOT EQUAL) and likely behaved in the way I mentioned it. As for the context size affecting the learning difference, I believe the smaller context size (as mentioned in the video) spits out garbage predictions forward and back equally terribly, making the loss equally bad in either direction. However, increasing the context size allows the model to understand the context a lot more and hit more roadbumps along the way, possibly adding up the bigger disparity between the losses/probabilities. I wished they tested out more languages before claiming it's universal, as we might find a language that is easier to learn backwards than forward, but I don't remember a language with a sentence structure unique enough to do so.

@@mesdamessoleils9869 I'm not quite sure how you computed the probabilities or why you even used that example to get the point across as it might not even be relevant to how a transformer works. Just curious though, how much experience do you have with knowing how transformers work inside out? I myself just learned recently and not 100% clear, nor am not sure of the model or the exact way they did it exactly, but if I have access to the source code, would probably be able to figure this out (rather just theories). However, judging by what I know, the model is trains and predicts a token based on the previous tokens passed into it. So even if I know that at the end of the word, "ing" happens more at the end of the word, I still would have more trouble predicting the root word ("learn" ) behind it rather than predicting "ing" comes after "learn". Just imagine it in terms of possible branches. Obviously, the more choices of likely words to choose from, the less probability for you to predict the next word correctly. Lets say make an example sentence, "I like learning math from my teacher" and the standard tokens are probably "I", "like", "learn", "ing", "math", "from", "my", "teacher". Moreover, assume that the model is trained with a bit more grammatically correct examples. Once my model generates up to the point, "I like learn", the next possible token that makes grammatically correct is easily going to be "ing" or something of high affinity if I use a different example. However, training it backwards, if I predicted "math from my teacher," I'm split between whether I should use a suffix ("ing") or ("learn") because each of them sounds grammatically plausible. Predicting backwards on a larger trained model, I can reasonably get the sentence "I like to learn math from my teacher" or "I like learning math from my teacher". As you can see, there are two plausible options predicting backwards which basically splits the probability of a confident prediction in two while going forwards, it most definitely is easier to complete the puzzle simply following the context clues (which GPTs are basically made for). I might not have exhausted all the cases, but you can probably see what I mean now. From that stand point, it's generally easier to predict forwards than backwards as you can see with english, and you can see this even more when you look at the syntactic structure of English. Generally speaking, we can predict that a good deal of english sentences start with a noun (aka subject or pronouns such as "I") while english sentences can end in a plethora of ways (nouns, verbs, words with suffixes which acts as a token of its own), making the amount of plausible choices that much more when trying to predict backwards. This mass of choices lowers the probability (aka certainty) that we have a confident right answer, hence unequal probabilities forward and back. Moreover, I think the video pretty much is mentioning what I am mentioning through various abstract examples, such as timestamp 6:36 for example. He pretty much says that it's much harder to predict the factors of a product rather than predict the product from the two factors, which completely makes sense. In essence, the models are struggling to learn backwards probably IS in fact since it's harder to learn/solve backwards, and the metric that shows that is the unequal joint probabilities of the sentence forward and back. I looked into the paper and video and found that the loss difference IS infact calculated by the joint probabilities instead, yet they are not the same. Moreover, the conditional probabilities are definitely most likely different forward and back given they are completely different conditional probabilities (NOT EQUAL) and likely behaved in the way I mentioned it. As for the context size affecting the learning difference, I believe the smaller context size (as mentioned in the video) spits out garbage predictions forward and back equally terribly, making the loss equally bad in either direction. However, increasing the context size allows the model to understand the context a lot more and hit more roadbumps along the way, possibly adding up the bigger disparity between the losses/probabilities. I wished they tested out more languages before claiming it's universal, as we might find a language that is easier to learn backwards than forward, but I don't remember a language with a sentence structure unique enough to do so.

@@mesdamessoleils9869 I'm not quite sure how you computed the probabilities or why you even used that example to get the point across as it might not even be relevant to how a transformer works. Just curious though, how much experience do you have with knowing how transformers work inside out? I myself just learned recently and not 100% clear, nor am not sure of the model or the exact way they did it exactly, but if I have access to the source code, would probably be able to figure this out (rather just theories). However, judging by what I know, the model is trains and predicts a token based on the previous tokens passed into it. So even if I know that at the end of the word, "ing" happens more at the end of the word, I still would have more trouble predicting the root word ("learn" ) behind it rather than predicting "ing" comes after "learn". Just imagine it in terms of possible branches. Obviously, the more choices of likely words to choose from, the less probability for you to predict the next word correctly. Lets say make an example sentence, "I like learning math from my teacher" and the standard tokens are probably "I", "like", "learn", "ing", "math", "from", "my", "teacher". Moreover, assume that the model is trained with a bit more grammatically correct examples. Once my model generates up to the point, "I like learn", the next possible token that makes grammatically correct is easily going to be "ing" or something of high affinity if I use a different example. However, training it backwards, if I predicted "math from my teacher," I'm split between whether I should use a suffix ("ing") or ("learn") because each of them sounds grammatically plausible. Predicting backwards on a larger trained model, I can reasonably get the sentence "I like to learn math from my teacher" or "I like learning math from my teacher". As you can see, there are two plausible options predicting backwards which basically splits the probability of a confident prediction in two while going forwards, it most definitely is easier to complete the puzzle simply following the context clues (which GPTs are basically made for). I might not have exhausted all the cases, but you can probably see what I mean now. From that stand point, it's generally easier to predict forwards than backwards as you can see with english, and you can see this even more when you look at the syntactic structure of English. Generally speaking, we can predict that a good deal of english sentences start with a noun (aka subject or pronouns such as "I") while english sentences can end in a plethora of ways (nouns, verbs, words with suffixes which acts as a token of its own), making the amount of plausible choices that much more when trying to predict backwards. This mass of choices lowers the probability (aka certainty) that we have a confident right answer, hence unequal probabilities forward and back. Moreover, I think the video pretty much is mentioning what I am mentioning through various abstract examples, such as timestamp 6:36 for example. He pretty much says that it's much harder to predict the factors of a product rather than predict the product from the two factors, which completely makes sense. In essence, the models are struggling to learn backwards probably IS in fact since it's harder to learn/solve backwards, and the metric that shows that is the unequal joint probabilities of the sentence forward and back. I looked into the paper and video and found that the loss difference IS infact calculated by the joint probabilities instead, yet they are not the same. Moreover, the conditional probabilities are definitely most likely different forward and back given they are completely different conditional probabilities (NOT EQUAL) and likely behaved in the way I mentioned it. As for the context size affecting the learning difference, I believe the smaller context size (as mentioned in the video) spits out garbage predictions forward and back equally terribly, making the loss equally bad in either direction. However, increasing the context size allows the model to understand the context a lot more and hit more roadbumps along the way, possibly adding up the bigger disparity between the losses/probabilities. I wished they tested out more languages before claiming it's universal, as we might find a language that is easier to learn backwards than forward, but I don't remember a language with a sentence structure unique enough to do so.

@@mesdamessoleils9869 I'm not quite sure how you computed the probabilities or why you even used that example to get the point across as it might not even be relevant to how a transformer works. Just curious though, how much experience do you have with knowing how transformers work inside out? I myself just learned recently and not 100% clear, nor am not sure of the model or the exact way they did it exactly, but if I have access to the source code, would probably be able to figure this out (rather just theories). However, judging by what I know, the model is trains and predicts a token based on the previous tokens passed into it. So even if I know that at the end of the word, "ing" happens more at the end of the word, I still would have more trouble predicting the root word ("learn" ) behind it rather than predicting "ing" comes after "learn". Just imagine it in terms of possible branches. Obviously, the more choices of likely words to choose from, the less probability for you to predict the next word correctly. Lets say make an example sentence, "I like learning math from my teacher" and the standard tokens are probably "I", "like", "learn", "ing", "math", "from", "my", "teacher". Moreover, assume that the model is trained with a bit more grammatically correct examples. Once my model generates up to the point, "I like learn", the next possible token that makes grammatically correct is easily going to be "ing" or something of high affinity if I use a different example. However, training it backwards, if I predicted "math from my teacher," I'm split between whether I should use a suffix ("ing") or ("learn") because each of them sounds grammatically plausible. Predicting backwards on a larger trained model, I can reasonably get the sentence "I like to learn math from my teacher" or "I like learning math from my teacher". As you can see, there are two plausible options predicting backwards which basically splits the probability of a confident prediction in two while going forwards, it most definitely is easier to complete the puzzle simply following the context clues (which GPTs are basically made for). I might not have exhausted all the cases, but you can probably see what I mean now. From that stand point, it's generally easier to predict forwards than backwards as you can see with english, and you can see this even more when you look at the syntactic structure of English. Generally speaking, we can predict that a good deal of english sentences start with a noun (aka subject or pronouns such as "I") while english sentences can end in a plethora of ways (nouns, verbs, words with suffixes which acts as a token of its own), making the amount of plausible choices that much more when trying to predict backwards. This mass of choices lowers the probability (aka certainty) that we have a confident right answer, hence unequal probabilities forward and back. Moreover, I think the video pretty much is mentioning what I am mentioning through various abstract examples, such as timestamp 6:36 for example. He pretty much says that it's much harder to predict the factors of a product rather than predict the product from the two factors, which completely makes sense. In essence, the models are struggling to learn backwards probably IS in fact since it's harder to learn/solve backwards, and the metric that shows that is the unequal joint probabilities of the sentence forward and back. I looked into the paper and video and found that the loss difference IS infact calculated by the joint probabilities instead, yet they are not the same. Moreover, the conditional probabilities are definitely most likely different forward and back given they are completely different conditional probabilities (NOT EQUAL) and likely behaved in the way I mentioned it. As for the context size affecting the learning difference, I believe the smaller context size (as mentioned in the video) spits out garbage predictions forward and back equally terribly, making the loss equally bad in either direction. However, increasing the context size allows the model to understand the context a lot more and hit more roadbumps along the way, possibly adding up the bigger disparity between the losses/probabilities. I wished they tested out more languages before claiming it's universal, as we might find a language that is easier to learn backwards than forward, but I don't remember a language with a sentence structure unique enough to do so.

Thanks Alfredo!

Very nice connection. I wonder how tokenization would affect this analysis. According to Sec. 2.1.1, the authors train a BPE tokenizer from scratch for each language individually. So even if French has a higher rate of spoken words per minute than English, perhaps the relevant statistic here would be "tokens per minute", since the reversal happens at the token level. For example, if it were the case that tokens per minute for the two languages ends up being similar, this would weaken this theory. These details are not examined in the paper but would definitely be interesting to see!

@@ariseffai Good point! I guess the average number of tokens per word is going to come down to how long French words tend to be compared to English words, and how repetitive the character combinations are, since they used the same total number of tokens when encoding both languages. Could definitely cancel out this effect, or even be the dominant cause of the difference itself!

Try Sanskrit

We tried that as well ! For one dataset, we trained the BPE tokenizer backwards, then made the experiment again with this tokenizer; If the asymmetry came from the tokenizer, you would expect the backward model to now do better; but it doesn't ! In fact, the loss curves for the 'reverse BPE' and 'forward BPE' tokenizers look almost identical. This means the arrow of time effect is not a result of the way you tokenize, but really a feature of the dataset. (BTW, we thought about char tokenizers, problem is with those it's very costly to train models with attention spanning more than a few sentences; since in that case a sentence is already 100s of tokens, and compute scales quadratically with attention)

Thanks! Appreciate the kind words.

r u 4 r3aL?

Not quite sure about that haha

Neat. Although one might also argue it should be easier in reverse because you can assume you will eventually reach a blank white canvas at the beginning of the video. But going forward, when you start with the blank white canvas, it is difficult to predict the exact scene that will be painted :)

Interesting! For me it was not a priori obvious. I like the sparsity argument from the paper as a potential mechanism, but I'd love to see concretely how one can prove language is "sparser" in the forward direction. The pronoun example has potential, but as @grapesurgeon mentions, there can often be forward references as well.

​@@grapesurgeon (Almost) all natural languages developed as a spoken language. It's much harder for the brain to build sentences that reference something that you will say three sentences later, because it would require you to already "build" the next three sentences in your head while you say the current sentence. Let's assume you currently "build" and say sentence A and next are B, C, D, etc. for A to reference B and C you'd also have them ready in your brain and thus B and C can't reference D, E, F or they would also influence how A is structured. There are some "high level" thoughts that do that, like "I'll tell you the details about that later..." but to say that you don't have to know the exact sentences you'll say later. But language itself (at least it feels obvious to me - I can't back any of that up) look like it has to have that structure and I assume even for advanced super human intelligence but probably with a larger time-frame/window. I think it boils down to that predicting the future is harder than storing/remembering the past. So it's simpler to reference something from the "exact" past than to reference something from the "exact" future because it's so hard to predict the "exact" future.

what are you even talking about?